\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz} 
%\usepackage[UTF8]{ctex}
%\usepackage{xeCJK}
\begin{document}
	$$
	\begin{pmatrix}
		x' & y'
	\end{pmatrix} 
	= 
	\begin{pmatrix}
		x & y
	\end{pmatrix}
	*
	\begin{bmatrix}
		a11 & a12 \\
		a21 & a22
	\end{bmatrix}
	$$
	
	$$
	\begin{bmatrix}
		a11 & a12 \\
		a21 & a22
	\end{bmatrix}
	=>
	\begin{bmatrix}
		1 & 0 \\
		1 & 1
	\end{bmatrix}
	$$
	
	$$
	\begin{pmatrix}
		0 & 0
	\end{pmatrix}
	,
	\begin{pmatrix}
		1 & 0
	\end{pmatrix}
	,
	\begin{pmatrix}
		0 & 1
	\end{pmatrix}
	,
	\begin{pmatrix}
		1 & 1
	\end{pmatrix}
	>
	\begin{pmatrix}
		x & y
	\end{pmatrix}
	$$
		
	$$
	\begin{tikzpicture}
        \draw (-0.5,0) -- (1.5,0); 
        \draw (0,-0.5) -- (0,1.5);
        \draw (0,0) rectangle (1,1);
%        \draw (0.5,0.5) circle [radius=0.5cm]
        \draw (0.25,0.25) rectangle (0.75,0.75);
        \filldraw (0.5,0.5) circle (.06);
    \end{tikzpicture}
	$$
	
	$$
	\begin{pmatrix}
		0 & 0
	\end{pmatrix}
	,
	\begin{pmatrix}
		1 & 0
	\end{pmatrix}
	,
	\begin{pmatrix}
		1 & 1
	\end{pmatrix}
	,
	\begin{pmatrix}
		2 & 1
	\end{pmatrix}
	>
	\begin{pmatrix}
		x' & y'
	\end{pmatrix}
	$$
	
	$$
	\begin{tikzpicture}
        \draw (-0.5,0) -- (1.5,0); 
        \draw (0,-0.5) -- (0,1.5);
%        \draw (0,0) rectangle (1,1);
		\draw[xshift =0pt ,xslant =1] (0,0) rectangle (1,1);
		\draw[xshift =0pt ,xslant =1] (0.25,0.25) rectangle (0.75,0.75);
        \filldraw (1,0.5) circle (.06);
    \end{tikzpicture}
	$$
	
	$$
	\begin{bmatrix}
		1 & 0 \\
		1 & 1
	\end{bmatrix}^{-1}
	=>
	\begin{bmatrix}
		1 & 0 \\
		-1 & 1
	\end{bmatrix}
	$$
	
	$$
	\begin{pmatrix}
		x' & y'
	\end{pmatrix}
	>
	\begin{pmatrix}
		x & y
	\end{pmatrix}
	$$
	
	$$
	\begin{pmatrix}
		1 & 1/2
	\end{pmatrix}
	>
	\begin{pmatrix}
		1/2 & 1/2
	\end{pmatrix}
	$$
\end{document}